Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach

References

  • Abate J., Whitt W. Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. (1995) 7:36–43LinkGoogle Scholar
  • Abramowitz M., Stegun I. A.Handbook of Mathematical Functions (1972) (Dover, New York) Google Scholar
  • Beaglehole D. R. Tax clienteles and stochastic processes in the gilt market. (1991) . Working paper, Graduate School of Business, University of Chicago, Chicago, ILGoogle Scholar
  • Black F., Scholes M. The pricing of options and corporate liabilities. J. Political Econom. (1973) 81:637–659CrossrefGoogle Scholar
  • Borodin A. N., Salminen P.Handbook of Brownian Motion (1996) (Birkhauser, Boston, MA) CrossrefGoogle Scholar
  • Boyle P. P., Tian Y. Pricing lookback and barrier options under the CEV process. J. Financial Quant. Anal. (1999) 34:241–264(correction: P. P. Boyle, Y. Tian, J. Imai. Lookback options under the CEV process: A correction. J. Financial Quant. Anal. website 〈http://depts.washington.edu/jfqa/〉 in Notes, Comments, and Corrections)CrossrefGoogle Scholar
  • Broadie M., Detemple J. American capped call options on dividend-paying assets. Rev. Financial Stud. (1995) 8:161–191CrossrefGoogle Scholar
  • Buchholz H.The Confluent Hypergeometric Function (1969) (Springer-Verlag, Berlin) CrossrefGoogle Scholar
  • Cox J. Notes on option pricing I:Constant elasticity of variance diffusions. . Working paper, Stanford University (reprinted in J. Portfolio Management, 1996, 22 15–17)Google Scholar
  • Cox J., Ross S. The valuation of options for alternative stochastic processes. J. Financial Econom. (1976) 3:145–166CrossrefGoogle Scholar
  • Cox J., Ingersoll J. E., Ross S. A. A theory of the term structure of interest rates. Econometrica (1985) 53:385–407CrossrefGoogle Scholar
  • Davydov D., Linetsky V. The valuation and hedging of barrier and lookback options under the CEV process. Management Sci. (2001) 47:949–965LinkGoogle Scholar
  • Davydov D., Linetsky V. Structuring, pricing and hedging double barrier step options. J. Comput. Finance (2001/2002) 5(2):55–87CrossrefGoogle Scholar
  • Doetsch G.Introduction to the Theory and Applications of the Laplace Transformation (1974) (Springer, New York) CrossrefGoogle Scholar
  • Duffie D. Price operators: Extensions, potentials, and the Markov valuation of securities. (1986) . Research paper 813, Graduate School of Business, Stanford University, Stanford, CAGoogle Scholar
  • Duffie D.Dynamic Asset Pricing (2001) 3rd ed.(Princeton University Press, Princeton, NJ) Google Scholar
  • Duffie D., Garman M. Intertemporal arbitrage and the Markov valuation of securities. (1986) . Working paper, Graduate School of Business, Stanford University, Stanford, CAGoogle Scholar
  • Dunford N., Schwartz J.Linear Operators. Part II: Spectral Theory (Self-Adjoint Operators in Hilbert Spaces) (1963) (Wiley, Hoboken, NJ) Google Scholar
  • Dynkin E. B.Markov Processes (1965) (Springer, Berlin, Germany) CrossrefGoogle Scholar
  • Emanuel D., MacBeth J. Further results on the constant elasticity of variance call option pricing model. J. Financial Quant. Anal. (1982) 17:533–554CrossrefGoogle Scholar
  • Erdelyi A.Higher Transcendental Functions (1953) II(McGraw-Hill, New York) Google Scholar
  • Ethier S. N., Kurtz T. G.Markov Processes: Characterization and Convergence (1986) (Wiley, New York) CrossrefGoogle Scholar
  • Florens J.-P., Renault E., Touzi N. Testing for embeddability by stationary reversible continuous-time Markov processes. Econometric Theory (1998) 14:744–769CrossrefGoogle Scholar
  • Fu M., Madan D., Wang T. Pricing Asian options: A comparison of analytical and Monte Carlo methods. J. Comput. Finance (1997) 2:49–74CrossrefGoogle Scholar
  • Fulton C., Pruess S. Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems. J. Math. Anal. Appl. (1994) 188:297–340CrossrefGoogle Scholar
  • Fulton C., Pruess S., Xie Y. The automatic classification of Sturm-Liouville problems. J. Appl. Math. Comput.Forthcoming 〈 http://www.mines.edu/fs_home/spruess/papers/class.psGoogle Scholar
  • Garman M. Towards a semigroup pricing theory. J. Finance (1985) XL:847–861CrossrefGoogle Scholar
  • Geman H., Yor M. Pricing and hedging double barrier options: A probabilistic approach. Math. Finance (1996) 6:365–378CrossrefGoogle Scholar
  • Giorno V., Nobile A. G., Ricciardi L. M., Sacerdote L. Some remarks on the Rayleigh process. J. Appl. Probab. (1986) 23:398–408CrossrefGoogle Scholar
  • Going-Jaeschke A., Yor M. A survey and some generalizations of Bessel processes. Bernoulli (2003) . in press 〈 http://www.risklab.ch/ftp/papers/GoeingYor.pdfGoogle Scholar
  • Goldstein R., Keirstead W. P. On the term structure of interest rates in the presence of reflecting and absorbing boundaries. (1997) . Working paper, Ohio State University, Columbus, OHGoogle Scholar
  • Gorovoi V., Linetsky V. Pricing step options under the CEV process. (2001) (Northwestern University, Evanston, IL) Google Scholar
  • Gorovoi V., Linetsky V. Black's model of interest rates as options, area functionals, eigenfunction expansions, and Japanese interest rates. Math. Finance (2003) . in pressGoogle Scholar
  • Gradshteyn I. S., Ryzhik I. M.Tables of Integrals, Series and Products (1994) (Academic Press, New York) Google Scholar
  • Hansen L. P., Scheinkman J. A., Touzi N. Spectral methods for identifying scalar diffusions. J. Econometrics (1998) 86:1–32CrossrefGoogle Scholar
  • Hull J.Options, Futures and Other Derivatives (2000) 4th ed.(Prentice-Hall, Englewood Cliffs, NJ) Google Scholar
  • Ito K., McKean H.Diffusion Processes and Their Sample Paths (1974) (Springer, Berlin, Germany) Google Scholar
  • Jackwerth J. C., Rubinstein M. Recovering stochastic processes from option prices. (1998) . Working paper, University of California, Berkeley, CAGoogle Scholar
  • Karatzas I., Shreve S. Brownian Motion and Stochastic Calculus, 2nd ed. (1991) (Springer-Verlag, New York) Google Scholar
  • Karlin S., Taylor H. M.A Second Course in Stochastic Processes (1981) (Academic Press, San Diego, CA) Google Scholar
  • Kunitomo N., Ikeda M. Pricing options with curved boundaries. Math. Finance (1992) 2:275–298CrossrefGoogle Scholar
  • Levitan B. M., Sargsjan I. S.Introduction to Spectral Theory (1975) (American Mathematical Society, Providence, RI) Google Scholar
  • Lewis A. Applications of eigenfunction expansions in continuous-time finance. Math. Finance (1998) 8:349–383CrossrefGoogle Scholar
  • Lewis A.Option Valuation Under Stochastic Volatility (1999) (Finance Press, Newport Beach, CA) Google Scholar
  • Linetsky V. Steps to the barrier. RISK (1998) April):62–65Google Scholar
  • Linetsky V. Step options. Math. Finance (1999) 9:55–96CrossrefGoogle Scholar
  • Linetsky V. Spectral expansions for Asian (average price) options. (2001) (Northwestern University, Evanston, IL) Google Scholar
  • Linetsky V. Exotic spectra. RISK (2002a) April):85–89Google Scholar
  • Linetsky V. Lookback options and diffusion hitting times: A spectral expansion approach. (2002b) (Northwestern University, Evanston, IL) Google Scholar
  • McKean H. Elementary solutions for certain parabolic partial differential equations. Trans. Amer. Math. Soc. (1956) 82:519–548CrossrefGoogle Scholar
  • Merton R. C. Theory of rational options pricing. Bell J. Econom. Management Sci. (1973) 4:141–183CrossrefGoogle Scholar
  • Pelsser A. Pricing double barrier options using analytical inversion of Laplace transforms. Finance Stochast (2000) 4:95–104CrossrefGoogle Scholar
  • Pryce D. J.Numerical Solution of Sturm-Liouville Problems (1993) (Clarendon, Oxford, U.K) Google Scholar
  • Prudnikov A. P., Brychkov Yu. A., Marichev O. I.Integrals and Series (1986) 2(Gordon and Breach, New York) Google Scholar
  • Reiner E. In search of parsimony: Valuing vanilla and exotic options for alternative stochastic processes. (1994) Derivatives ConferenceToronto, Ontario, CanadaGoogle Scholar
  • Schoutens W.Stochastic Processes and Orthogonal Polynomials (2000) (Springer, New York) CrossrefGoogle Scholar
  • Schroder M. Computing the constant elasticity of variance option pricing formula. J. Finance (1989) 44:211–219CrossrefGoogle Scholar
  • Schroder M. On the valuation of double-barrier options: Computational aspects. (1999) . Preprint, University of Mannheim, Mannheim, GermanyGoogle Scholar
  • Shiga T., Watanabe S. Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrscheinlichkeitstheorie Verw. Geb. (1973) 27:37–46CrossrefGoogle Scholar
  • Slater L. J.Confluent Hypergeometric Functions (1960) (Cambridge University Press, U.K) Google Scholar
  • Stakgold I.Green's Functions and Boundary Value Problems (1998) 2nd ed.(Wiley, New York) Google Scholar
  • Titchmarsh E. C.Eigenfunction Expansions Associated with Second-Order Differential Equations (1962) (Clarendon, Oxford, U.K) Google Scholar
  • Weyl H. Uber gewohncliche lineare differentialgleichungen mit singularitaten und die zugehorigen entwicklungen wilkurlicher funktionen. Math. Ann. (1910) 68:220–269CrossrefGoogle Scholar
  • Wong E., Bellman R. The construction of a class of stationary Markoff processes. Sixteenth Symposium in Applied Mathematics–Stochastic Processes in Mathematical Physics and Engineering (1964) (American Mathematical Society, Providence, RI) 264–276CrossrefGoogle Scholar
  • Zhang P.Exotic Options (1997) (World Scientific, Singapore) CrossrefGoogle Scholar
  • Zwillinger D.Handbook of Differential Equations (1998) (Academic Press, San Diego, CA) Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.